Using Cramer's Rule to find needed equations

  • Thread starter Final9mare
  • Start date
  • #1

Homework Statement


I am finding the minimum coefficient μ between tires and road so that cars do not slide off. I have my equations for ƩFy and ƩFx and I know μ = [fs]/[/N]

So I would need to use cramer's rule on my equations to find fs and N.

But I am not sure how to use cramer's rule for my equations.


Homework Equations


ƩFx = Nsinθ -fscosθ = mv2/r
ƩFy = Ncosθ + fssinθ = mg

The Attempt at a Solution


I actually already have the answer but im not sure how to use cramer's to get to it.

fs = m(gsinθ-v2/r*cosθ)

N = m(v2/r*sinθ+gcosθ)
 

Answers and Replies

  • #2
haruspex
Science Advisor
Homework Helper
Insights Author
Gold Member
2020 Award
36,756
7,099
At a guess (which I should not be needing to do!) the car is negotiating a bend radius r, banked at angle theta (in the helpful direction).
ƩFx = Nsinθ -fscosθ = mv2/r
ƩFy = Ncosθ + fssinθ = mg
Sure about the sign of fs in those? Or is this calculating the minimum speed?
I actually already have the answer but im not sure how to use cramer's to get to it.
fs = m(gsinθ-v2/r*cosθ)
N = m(v2/r*sinθ+gcosθ)
You have two equations and two unknowns. You're accustomed to dealing with pairs of simultaneous equations, I trust.
 

Related Threads on Using Cramer's Rule to find needed equations

  • Last Post
Replies
3
Views
2K
Replies
3
Views
1K
Replies
5
Views
3K
Replies
3
Views
1K
Replies
5
Views
5K
  • Last Post
Replies
17
Views
3K
Replies
1
Views
729
Replies
2
Views
17K
Replies
6
Views
951
Top